Question: The sum of two numbers is $37$, and their difference is $15$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 37}$ ${x-y = 15}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 52 $ $ x = \dfrac{52}{2} $ ${x = 26}$ Now that you know ${x = 26}$ , plug it back into $ {x+y = 37}$ to find $y$ ${(26)}{ + y = 37}$ ${y = 11}$ You can also plug ${x = 26}$ into $ {x-y = 15}$ and get the same answer for $y$ ${(26)}{ - y = 15}$ ${y = 11}$ Therefore, the larger number is $26$, and the smaller number is $11$.